U.S. patent application number 13/890686 was filed with the patent office on 2014-11-13 for diffraction leveraged modulation of x-ray pulses using mems-based x-ray optics.
This patent application is currently assigned to UChicago Argonne, LLC. The applicant listed for this patent is UChicago Argonne, LLC. Invention is credited to Il-Woong Jung, Daniel Lopez, Deepkishore Mukhopadhyay, Gopal Shenoy, Donald A. Walko, Jin Wang.
Application Number | 20140334607 13/890686 |
Document ID | / |
Family ID | 51864791 |
Filed Date | 2014-11-13 |
United States Patent
Application |
20140334607 |
Kind Code |
A1 |
Lopez; Daniel ; et
al. |
November 13, 2014 |
DIFFRACTION LEVERAGED MODULATION OF X-RAY PULSES USING MEMS-BASED
X-RAY OPTICS
Abstract
A method and apparatus are provided for implementing
Bragg-diffraction leveraged modulation of X-ray pulses using
MicroElectroMechanical systems (MEMS) based diffractive optics. An
oscillating crystalline MEMS device generates a controllable
time-window for diffraction of the incident X-ray radiation. The
Bragg-diffraction leveraged modulation of X-ray pulses includes
isolating a particular pulse, spatially separating individual
pulses, and spreading a single pulse from an X-ray pulse-train.
Inventors: |
Lopez; Daniel; (Chicago,
IL) ; Shenoy; Gopal; (Naperville, IL) ; Wang;
Jin; (Burr Ridge, IL) ; Walko; Donald A.;
(Woodridge, IL) ; Jung; Il-Woong; (Woodridge,
IL) ; Mukhopadhyay; Deepkishore; (Ventura,
CA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
UChicago Argonne, LLC |
Chicago |
IL |
US |
|
|
Assignee: |
UChicago Argonne, LLC
Chicago
IL
|
Family ID: |
51864791 |
Appl. No.: |
13/890686 |
Filed: |
May 9, 2013 |
Current U.S.
Class: |
378/145 |
Current CPC
Class: |
G21K 1/06 20130101; G21K
2201/062 20130101 |
Class at
Publication: |
378/145 |
International
Class: |
G21K 1/06 20060101
G21K001/06 |
Goverment Interests
CONTRACTUAL ORIGIN OF THE INVENTION
[0001] The United States Government has rights in this invention
pursuant to Contract No. DE-AC02-06CH11357 between the United
States Government and UChicago Argonne, LLC representing Argonne
National Laboratory.
Claims
1. A method for implementing Bragg-diffraction leveraged modulation
of X-ray pulses using MicroElectroMechanical systems (MEMS) based
diffractive optics comprising: providing an oscillating crystalline
MEMS device; providing incident X-ray radiation on the oscillating
crystalline MEMS device; and generating a controllable time-window
of selected pulses with Bragg-diffraction leveraged modulation of
the incident X-ray radiation using the oscillating crystalline MEMS
device.
2. The method as recited in claim 1, wherein providing incident
X-ray radiation on the oscillating crystalline MEMS device includes
providing hard X-ray pulses from a synchrotron radiation
source.
3. The method as recited in claim 1 wherein providing an
oscillating crystalline MEMS device includes providing a
controllably oscillated crystalline MEMS device by providing a
selected oscillation frequency.
4. The method as recited in claim 3 includes changing said
controllable time-window of selected pulses by providing said
selected oscillation frequency.
5. The method as recited in claim 3 wherein providing said selected
oscillation frequency includes providing a pair of comb-drive
actuators together with respective torsional flexures for driving
an X-ray diffractive crystal.
6. The method as recited in claim 1 wherein generating a
controllable time-window of selected pulses with Bragg-diffraction
leveraged modulation of the incident X-ray radiation using the
oscillating crystalline MEMS device includes diffracting X-ray
pulses during an oscillation cycle of the oscillating crystalline
MEMS device when the incident X-ray radiation has an angle of
incidence equal to a Bragg angle .theta..sub.B for the oscillating
crystalline MEMS device.
7. The method as recited in claim 1 wherein generating a
controllable time-window of selected pulses with Bragg-diffraction
leveraged modulation of the incident X-ray radiation using the
oscillating crystalline MEMS device includes providing the incident
X-ray radiation on the oscillating crystalline MEMS device
including an incident X-ray pulse train.
8. The method as recited in claim 7 includes providing an angle of
incidence equal to a Bragg angle .theta..sub.B for the oscillating
crystalline MEMS device for isolating predefined pulses, and
spatially separating the selected pulses.
9. The method as recited in claim 7 includes providing a selected
oscillation frequency for the oscillating crystalline MEMS device
for isolating predefined pulses, and spatially separating the
selected pulses.
10. The method as recited in claim 7 includes providing an angle of
incidence equal to a Bragg angle .theta..sub.B for the oscillating
crystalline MEMS device and providing a selected oscillation
frequency for the oscillating crystalline MEMS device for spreading
a single pulse from an X-ray pulse-train.
11. The method as recited in claim 1 wherein providing said
oscillating crystalline MEMS device includes fabricating said
oscillating crystalline MEMS device using a Silicon-On-Insulator
(SOI) wafer for providing a single-crystal-silicon, and removing a
substrate beneath the single-crystal-silicon.
12. The method as recited in claim 11 wherein fabricating said
oscillating crystalline MEMS device includes providing a pair of
torsional flexures coupled to single-crystal-silicon and anchored
to the substrate.
13. The method as recited in claim 12 includes providing a
respective pair of comb-drive actuators coupled to the pair of
torsional flexures.
14. The method as recited in claim 11 includes providing said
comb-drive actuators with inter-digitated capacitors (IDCs).
15. An apparatus for implementing Bragg-diffraction leveraged
modulation of X-ray pulses using MicroElectroMechanical systems
(MEMS) based diffractive optics comprising: an oscillating
crystalline MEMS device; an X-ray source providing incident X-ray
radiation on the oscillating crystalline MEMS device; and said
oscillating crystalline MEMS device generating a controllable
time-window of selected pulses with Bragg-diffraction leveraged
modulation of the incident X-ray radiation.
16. The apparatus as recited in claim 15 wherein said oscillating
crystalline MEMS device includes a Silicon-On-Insulator (SOI) wafer
including a single-crystal-silicon forming an X-ray diffractive
crystal, a substrate being removed below the
single-crystal-silicon.
17. The apparatus as recited in claim 16 wherein said oscillating
crystalline MEMS device includes a respective pair of torsional
flexures coupled to said single-crystal-silicon and said
substrate.
18. The apparatus as recited in claim 17 wherein said oscillating
crystalline MEMS device includes a respective pair of comb-drive
actuators coupled to the pair of torsional flexures, said
comb-drive actuators including inter-digitated capacitors
(IDCs).
19. The apparatus as recited in claim 15 wherein said oscillating
crystalline MEMS device provides Bragg-diffraction leveraged
modulation of X-ray pulses including isolating a single pulse,
spatially separating individual pulses, and spreading a single
pulse from an X-ray pulse-train.
20. The apparatus as recited in claim 13 wherein said an X-ray
source includes a synchrotron radiation source providing hard X-ray
pulses to said oscillating crystalline MEMS device.
Description
FIELD OF THE INVENTION
[0002] The present invention relates generally to the temporal
modulation of X-rays, and more particularly, relates to a method
and apparatus for implementing Bragg-diffraction leveraged
modulation of X-ray pulses using MicroElectroMechanical systems
(MEMS) based diffractive optics.
DESCRIPTION OF THE RELATED ART
[0003] U.S. patent application Ser. No. 13/246,008 filed Sep. 27,
2011, entitled "METHOD FOR SPATIALLY MODULATING X-RAY PULSES USING
MEMS-BASED X-RAY OPTICS" by Daniel Lopez et al., the present
inventors, and assigned to the present assignee, discloses a method
and apparatus for spatially modulating X-rays or X-ray pulses using
MicroElectroMechanical or microelectromechanical systems (MEMS)
based X-ray optics including oscillating MEMS micromirrors. A
torsionally-oscillating MEMS micromirror and a method of leveraging
the grazing-angle reflection property are provided to modulate
X-ray pulses with a high-degree of controllability.
[0004] Modern materials of technological importance are replete
with cyclical and nonequilibrium processes that span multiple
time-scales ranging from milliseconds to femtoseconds. They
include, for example, next-generation denser and faster information
storage devices, catalysts responsible for energy conversion, or
optogenetic devices used for neurobiological control. A fundamental
understanding of the ultrafast dynamics of charge-, spin- and
atomic-organization in these materials is essential to understand
the processes and to control them to attain the desired functions.
The availability of synchrotron radiation X-ray sources during the
past decade, especially the development of X-ray
free-electron-lasers (XFELs), has allowed the probing of these
processes with femtosecond to picosecond resolution following the
excitation by an energy stimulus (pump) from an optical laser or a
magnetic/electric pulse generator or a THz source.
[0005] Recently, there has been an overwhelming interest in
exploring time-domain science using X-ray pulses generated by
synchrotron radiation sources. The unique properties of X-ray
pulses (duration, pulse train, and the like) from these sources can
be enhanced using ultrafast MEMS-based X-ray optics. A need exists
to develop such ultrafast MEMS-based X-ray diffractive optics.
[0006] A need exists for a method and apparatus for implementing
Bragg-diffraction leveraged modulation of X-ray pulses using
MicroElectroMechanical systems (MEMS) based X-ray diffractive
optics. It is desirable to provide such MEMS based diffractive
optics to control the delivery of hard X-ray pulses from a
synchrotron radiation source. It is desirable to provide such
method and apparatus for implementing Bragg-diffraction leveraged
modulation of X-ray pulses that achieves a narrow width of the
diffractive time-widow from high angular velocity of the MEMS based
X-ray diffractive optics.
SUMMARY OF THE INVENTION
[0007] Principal aspects of the present invention are to provide a
method and apparatus for implementing Bragg-diffraction leveraged
modulation of X-ray pulses using MicroElectroMechanical systems
(MEMS) based diffractive optics. Other important aspects of the
present invention are to provide such method and apparatus
substantially without negative effect and that overcome some of the
disadvantages of prior art arrangements.
[0008] In brief, a method and apparatus are provided for
implementing Bragg-diffraction leveraged modulation of X-ray pulses
using MicroElectroMechanical systems (MEMS) based diffractive
optics. An oscillating crystalline MEMS device generates a
controllable time-window for diffraction of the incident X-ray
radiation. A narrow width of the diffractive time-widow is achieved
by a selected angular velocity of the MEMS device.
[0009] In accordance with features of the invention, the
oscillating crystalline MEMS device includes a single-crystal MEMS
that can diffract or transmit X-ray radiation by changing its
relative orientation to the incident X-ray beam. The oscillating
MEMS device diffracts the X-ray pulses over a short period of time
when the Bragg condition is satisfied.
[0010] In accordance with features of the invention, the
oscillating crystalline MEMS device with a high angular velocity,
for example, of 1.262.degree./.mu.s (microsecond) sorts consecutive
X-ray pulses with a separation as close as 2.8.+-.0.4 ns
(nanosecond). The MEMS angular speed determines the width of the
diffractive time window over which the Bragg condition is
fulfilled.
[0011] In accordance with features of the invention, the MEMS based
X-ray diffractive optics includes a single-crystal-silicon (SCS)
device layer formed on a Silicon-On-Insulator (SOI) wafer, using
conventional semiconductor fabrication technique. The substrate
beneath the crystal is removed to allow large out-of-plane
oscillations and to allow transmission of X-rays.
[0012] In accordance with features of the invention, the MEMS based
X-ray diffractive optics includes in-plane comb-drive actuators,
formed by, for example, inter-digitated capacitors (IDCs).
BRIEF DESCRIPTION OF THE DRAWINGS
[0013] The present invention together with the above and other
objects and advantages may best be understood from the following
detailed description of the preferred embodiments of the invention
illustrated in the drawings, wherein:
[0014] FIGS. 1A and 1B schematically illustrate respectively
example MEMS X-ray optics apparatus for implementing
Bragg-diffraction leveraged modulation of X-ray pulses and example
Bragg diffraction leveraged modulation operation in accordance with
preferred embodiments;
[0015] FIGS. 1C, and 1D and FIGS. 1E, and 1F respectively
illustrate angular velocity of the MEMS together with a varied
diffractive timing window for higher and lower angular velocity in
accordance with preferred embodiments;
[0016] FIGS. 2A and 2B schematically illustrate respectively
example MEMS diffractive optics apparatus for implementing
Bragg-diffraction leveraged modulation of X-ray pulses and an
example static rocking curve with Bragg diffracted pulses
.theta.-.theta..sub.B (.degree.) shown relative the horizontal axis
and reflectivity shown relative the vertical axis showing a
prominent Si(400) diffraction peak at 8 keV with nearly 50%
reflectivity and broad peaks on the right which originate from
lattice strain in accordance with a preferred embodiment;
[0017] FIGS. 3A, 3B, 3C, and 3D illustrate respective example
dynamic performance of the MEMS diffractive optics in accordance
with preferred embodiments; and
[0018] FIG. 4 illustrates an example X-ray diffractive time window
achieved with a MEMS based diffractive optics with time in
nanoseconds (ns) shown relative the horizontal axis and intensity
(arbitrary units) shown relative the vertical axis in accordance
with preferred embodiments.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0019] In the following detailed description of embodiments of the
invention, reference is made to the accompanying drawings, which
illustrate example embodiments by which the invention may be
practiced. It is to be understood that other embodiments may be
utilized and structural changes may be made without departing from
the scope of the invention.
[0020] The terminology used herein is for the purpose of describing
particular embodiments only and is not intended to be limiting of
the invention. As used herein, the singular forms "a", "an" and
"the" are intended to include the plural forms as well, unless the
context clearly indicates otherwise. It will be further understood
that the terms "comprises" and/or "comprising," when used in this
specification, specify the presence of stated features, integers,
steps, operations, elements, and/or components, but do not preclude
the presence or addition of one or more other features, integers,
steps, operations, elements, components, and/or groups thereof.
[0021] In accordance with features of the invention, a method and
apparatus are provided for implementing Bragg-diffraction leveraged
modulation of X-ray pulses using MicroElectroMechanical (MEMS)
based X-ray diffractive optics. The novel MEMS X-ray diffractive
apparatus of the invention provides a crucial capability in
investigating dynamical processes in biological, chemical and
energy materials, and provides a new method to manipulate pulse
shape at the present and future X-ray sources, such as X-ray
free-electron-lasers (XFELs).
[0022] Having reference now to the drawings, in FIG. 1A, there is
schematically shown example MEMS X-ray diffractive apparatus for
implementing Bragg-diffraction leveraged modulation of X-ray pulses
generally designated by the reference character 100 in accordance
with preferred embodiments. MEMS X-ray diffractive apparatus 100
includes a MicroElectroMechanical (MEMS) based X-ray diffractive
optics 102 used in the X-ray wavelength range as diffractive
optics.
[0023] MEMS X-ray diffractive apparatus 100 includes an X-ray
source providing an X-ray radiation such as an X-ray beam, for
example, a synchrotron storage-ring 104, such as the Advanced
Photon Source (APS) at Argonne National Laboratory. The X-ray beam
is monochromatized by a double-crystal monochromator 106, spatially
filtered by an aperture 108, diffracted by the MEMS 102 and
collected by a detector 110.
[0024] Referring also to FIG. 1B, Bragg diffraction leveraged
modulation operation generally designated by the reference
character 112 is illustrated in accordance with preferred
embodiments. Diffraction of x-ray pulses is realized by placing the
MEMS Si-single-crystal in the Bragg condition depending on the
energy of the X-rays and the diffraction plane. Incoming pulses
applied to the MEMS based X-ray diffractive optics 102 are
diffracted when the Bragg condition is satisfied during the dynamic
rotation of the crystal, represented by diffracted pulses when
.theta.=.theta..sub.B. When the Bragg condition is not satisfied
during the dynamic rotation of the crystal, the X-ray pulses are
either absorbed or transmitted.
[0025] In accordance with features of the invention, the MEMS
angular speed determines the width of the diffractive time window
over which the Bragg condition is fulfilled.
[0026] FIGS. 1C, and 1D and FIGS. 1E, and 1F respectively
illustrate angular velocity of the MEMS and a varied diffractive
timing window for higher and lower angular velocity in accordance
with preferred embodiments.
[0027] Referring to FIGS. 1C, and 1D, a higher angular velocity 114
is illustrated in FIG. 1C and diffraction of x-ray pulses is
realized by placing the MEMS Si-single-crystal 102 in the Bragg
condition. In FIG. 1D, an example diffractive time window generally
designated by the reference character 116 is illustrated for the
higher angular velocity 114 of the MEMS device 102.
[0028] Referring to FIGS. 1E, and 1F, a lower angular velocity 118
is illustrated in FIG. 1E and diffraction of x-ray pulses is
realized by placing the MEMS Si-single-crystal 102 in the Bragg
condition. In FIG. 1F, an example diffractive time window generally
designated by the reference character 120 is illustrated for the
lower angular velocity 118 of the MEMS device 102. An illustrated
width, .DELTA.t.sub.w, of the illustrated diffractive time window
120 is increased or stretched as compared to the illustrated width,
.DELTA.t.sub.w, of the illustrated diffractive time window 116
resulting from the lower angular velocity.
[0029] FIGS. 2A and 2B schematically illustrate respective example
MEMS diffractive optics apparatus for implementing
Bragg-diffraction leveraged modulation of X-ray pulses and an
example static rocking curve shows a prominent Si(400) diffraction
peak at 8 keV with nearly 50% reflectivity and broad peaks on the
right which originate from the lattice strain in accordance with a
preferred embodiment.
[0030] Referring to FIG. 2A, an electron microscopy image is
provided of an example MEMS based diffractive optics device
generally designated by the reference character 200 used for
implementing Bragg-diffraction leveraged modulation in accordance
with preferred embodiments. MEMS based diffractive optics device
200 includes a single X-ray diffractive crystal 202, such as a
Si(100) crystal with dimensions of 500 .mu.m (long).times.250 .mu.m
(wide).times.25 .mu.m (thick) suspended by a pair of torsional
flexures 204, 206, which are anchored to a substrate 208. The
flexures 204, 206 allow the crystal 202 to rotate in the torsional
oscillation mode about an axis joining the anchors. The MEMS device
202 is fabricated using a SOI (silicon-on-insulator) wafer, which
provides the single-crystal-silicon 202 necessary to diffract
x-rays. The substrate 208 beneath the crystal is removed to allow
large out-of-plane oscillations and to allow transmission of
X-rays. The excitation is provided by in-plane comb-drive actuators
210, which are implemented, for example, by inter-digitated
capacitors (IDCs) that provide torque with large force density.
[0031] Referring to FIG. 2B, a typical rocking curve of the crystal
is shown generally designated by the reference character 220 with a
peak reflectivity close to 50%. It consists of a narrow and intense
Si(400) peak and additional intensity in the broad peaks above
.theta..sub.B. The static rocking curve shows a prominent Si(400)
diffraction peak at 8 keV with nearly 50% reflectivity and broad
peaks on the right which originate from the lattice strain.
[0032] In FIG. 2B, these illustrated broad peaks originate from the
lattice strain due to shallow diffusive phosphorous dopant layers
introduced on the crystal surface during the MEMS fabrication.
Since the X-ray diffractive properties of these dopant layers are
not known, the intensity was fitted with two Gaussian peaks
centered at 0.0038.degree. and 0.0091.degree. above the Si(400)
peak. The large angular separation of these two shoulder peaks from
the Si(400) peak and their lower intensities allowed an accurate
analysis of the Si(400) peak. The line representing Si(400) peak
shown in FIG. 2B, also modeled as a Gaussian, has a
full-width-at-half-maximum (FWHM), .DELTA..theta..sub.(400) of
0.0034.degree. (59 microradians). An analysis of the diffraction
profile yields an extremely good fit to the measured data as shown
in FIG. 2B. Parenthetically, it should be understood that
dopant-induced strain can be eliminated in the future by
appropriately modifying the MEMS fabrication process.
[0033] FIGS. 3A, 3B, 3C, and 3D illustrate respective example
dynamic performance of the MEMS diffractive optics in accordance
with preferred embodiments.
[0034] In FIG. 3A, normalized angular velocity generally designated
by the reference character 300 over one oscillating cycle of MEMS,
where .omega..sub.max=1.262.degree./.mu.s.
[0035] In FIG. 3B, experimental data generally designated by the
reference character 320 is shown in the time domain where the
position and intensity of the 8 keV diffracted X-ray peaks (locally
expanded along the time axis by a factor of 20) over the
oscillation cycle is plotted as a function of time over the
oscillation period and the values of .DELTA..theta.. The diffracted
peak is narrowest when .DELTA..theta.=0. The mirror image of
diffraction profiles on the two branches of motion highlights the
symmetric motion of the MEMS device 102.
[0036] In FIG. 3C, illustrated data generally designated by the
reference character 330 shows measured values dots and calculation
with the measured time gap between the X-ray pulses fits perfectly
with the following Eq. (2) set forth below when the maximum value
of the MEMS deflection is .+-.2.69.degree..
[0037] In FIG. 3D, illustrated data generally designated by the
reference character 340 shows measured values dots and calculation
with a width, .DELTA.t.sub.w, of Si(400) diffraction peak obtained
from the time-domain diffraction profiles analyzed using the
3-Gaussian model shown as a function of .DELTA..theta.. The
measured values dots deviate from the following Eq. (3) set forth
below represented by a solid line curve indicating increased
dynamic distortion of the MEMS when deviating further from
.DELTA..theta.=0.
[0038] Operation of the apparatus 100 and MEMS based diffractive
optics device 200 of the invention may be understood as follows.
When the crystal is strain and defect free, the value of
.DELTA..theta..sub.(400) is determined by a convolution between the
angular and energy widths of the incoming monochromatic beam and
the Darwin width of the Si(400) crystal which was calculated to be
0.0028.degree. (49 microradians). The measured
.DELTA..theta..sub.(400) is about 20% broader, which can be
accounted from the static deformation strain of the suspended
25-.mu.m thick MEMS crystal. The static deformation of
0.0014.degree. (24 microradians) was estimated from the measured
concave curvature of the crystal from both optical and X-ray data.
This broadens the rocking curve width to 0.0032.degree. (55
microradians) in good agreement with the measured value. This
detailed analysis of the static rocking curve ascertained that the
MEMS is well suited as an X-ray diffractive optics.
[0039] When the MEMS is so aligned that the X-ray incident angle is
.theta..sub.0 when crystal element is stationary, the time
dependence of the incident angle .theta. during the oscillation can
be described as .theta.(t)=.theta..sub.0+.alpha..sub.m
cos(2.pi.f.sub.mt). The angular velocity of MEMS, .omega.(t), is
given by:
.omega.(t)=.omega..sub.max sin(2.pi.f.sub.mt) (1)
where .omega..sub.max=2.pi.f.sub.m.alpha..sub.m is the maximum
angular velocity of by the MEMS. The incident X-ray beam is
diffracted at the Bragg condition, .theta.(t)=.theta..sub.B, and
that occurs twice in an oscillation cycle. The value of
|.omega.(t)/.omega..sub.max| is unity at T/4 and 3T/4 as shown in
FIG. 3A, where T=1/f.sub.m is the oscillation period.
[0040] For a crystal with a rocking curve width
.DELTA..theta..sub.(hkl) (for diffraction plane hkl), the gap
between two consecutive diffraction-windows (in an oscillation
cycle), .DELTA.t.sub.g, and the width of the
diffraction-time-window, .DELTA.t.sub.w, are dependent on the
angular offset defined by
.DELTA..theta. = .theta. B - ? , ? indicates text missing or
illegible when filed ##EQU00001##
and given by,
.DELTA. t g = 1 f m - cos - 1 ( .DELTA. .theta. .alpha. m ) ( .pi.
f m ) ( 2 ) ##EQU00002##
[0041] And, where
? = ? 2 .pi. f m .alpha. m 1 - ( .DELTA. .theta. .alpha. m ) 2 . ?
indicates text missing or illegible when filed ( 3 )
##EQU00003##
[0042] From these equations it can be noted that the smallest width
of the diffraction-time-window,
? 2 .pi. f m .alpha. m , ? indicates text missing or illegible when
filed ##EQU00004##
is obtained when
.DELTA..theta. = 0 ( ? = .theta. B ) ##EQU00005## ? indicates text
missing or illegible when filed ##EQU00005.2##
corresponding to gap between pulses of 1/(2f.sub.m).
[0043] The dynamic performance of the MEMS is evaluated from X-ray
intensity measurements in the time domain by subjecting it to the
incident X-ray pulse-train during the APS standard operating mode
in which the pulse-to-pulse separation is 153.4 ns. The MEMS is
driven by a 70 V.sub.pp actuation signal with frequency
2f.sub.m(f.sub.m=74.671 kHz), resulting in a harmonic oscillation
with a nominal amplitude .alpha..sub.m=.+-.3.degree. and period (T)
of 13.392 .mu.s. During each MEMS oscillation cycle, only the X-ray
pulses that satisfy the Bragg condition over a defined Si(400)
diffractive time window will be diffracted.
[0044] In an experiment, the time dependence of the 8 keV
diffracted X-ray intensities were collected for different values of
.DELTA..theta. by a fast-response avalanche photodiode detector
(APD) operating in a charge-integrating mode, as further described
below in an example method of operation. The profile of the
diffractive time window is constructed by varying the arrival time
of the X-ray pulses with respect to the MEMS driving signal. The
measured diffractive window in the time domain is shown in FIG. 3B
as a function of .DELTA..theta.. Since .DELTA.t.sub.w is only
several nanoseconds, the intensity traces in FIG. 3B are plotted in
an expanded time scale by a factor of 20 to make their shapes
clearly visible.
[0045] The traces shown in FIG. 3B emphasize symmetrical
performance of the MEMS in an oscillation cycle. Along the vertical
axis, the intensity peaks are offset by the amount of
.DELTA..theta., ranging from -2.4.degree. to +2.0.degree., within
the nominal oscillation amplitude of the MEMS. The intensity peaks
are clearly in two branches, corresponding to the two instances in
time when Bragg condition was met within an oscillatory cycle from
two rotation directions. Their position on the plot is denoted by
the solid dots in FIG. 3B. The two critical dynamic parameters,
.DELTA.t.sub.g and .DELTA.t.sub.w, can be derived from the
diffraction peaks, as is illustrated in FIG. 3B. The values of
.DELTA.t.sub.g are plotted in FIG. 3C as a function of
.DELTA..theta., along with a fit (solid line) using Eq. (2). The
remarkable agreement between the data and the fit allowed accurate
and independent determination of the MEMS oscillation amplitude,
.alpha..sub.m=.+-.(2.692..+-.0.01).degree., the only fitting
parameter in the equation. As reflected in Eqs. (1)-(3), this is
the most critical parameter necessary to describe all the dynamic
properties of the MEMS.
[0046] The diffraction profiles shown in FIG. 3B as a function
.DELTA..theta. (and the mirror images) retain the features measured
in the static rocking curve FIG. 2B). However the width of the
Si(400) peak (or .DELTA.t.sub.w) varies with .DELTA..theta. and in
fact, it is inversely proportional to the angular velocity of the
MEMS, as expected from Eq. (3). Of all the peaks in the profiles,
the narrowest and highest intensity peaks occurs when
.DELTA..theta. equals 0 (.DELTA..theta.=0) at which the MEMS
reaches the maximum angular velocity
.omega..sub.max=1.262.degree./.mu.s.
[0047] It is important to notice that this angular velocity is
nearly an order of magnitude higher than that of a flywheel, and is
achieved with an order of magnitude lower linear velocity. The peak
narrows when the angular velocity increases (FIGS. 3A, 3B and FIGS.
1C, 1D) and its intensity increases as |.DELTA..theta.| decreases
(FIG. 3B). Therefore, the time-domain diffraction profiles can be
analyzed with confidence using the 3-Gaussian model (used to fit
the static rocking curve in FIG. 2B) to extract the width
.DELTA.t.sub.w of the most prominent Si(400) diffraction peak. The
values of .DELTA.t.sub.w are shown as a function of .DELTA..theta.
in FIG. 3D, along with calculated values (solid line) using Eq. (3)
with no adjustable parameters. Within experimental error, the data
are adequately accounted for at .DELTA..theta.=0 by Eq. (3),
without introducing additional strain-related broadening of the
rocking curve, demonstrating negligible dynamic distortion of the
MEMS at this X-ray incident angle. Away from this condition,
measured .DELTA.t.sub.w departs rapidly from that predicted by Eq.
(3), suggesting that the broadening of .DELTA..theta..sub.(400)
stems from growing amount of strain introduced by dynamic
deformation.
[0048] To highlight the narrowest diffractive window achieved with
the MEMS optics, the measured dynamic diffraction profile at
.DELTA..theta.=0 is shown in detail in FIG. 4, along with a
3-Gaussian fit. The resulting .DELTA.t.sub.w corresponding to the
prominent Si(400) peak is 2.8.+-.0.4 ns. This is in excellent
agreement with the value of 2.7 ns obtained from Eq. (3) using
experimentally obtained value of
.DELTA..theta..sub.(400)=0.0034.degree.,
.alpha..sub.m=.+-.2.69.degree., and f.sub.m=74.671 kHz.
[0049] Referring also to FIG. 4, there is shown an example X-ray
diffractive time window generally designated by the reference
character 400 achieved with the MEMS based diffractive optics 102,
200. In FIG. 4, time in nanoseconds (ns) is shown relative the
horizontal axis and intensity (arbitrary units) shown relative the
vertical axis in accordance with preferred embodiments. The
measured dynamic diffraction profile (dots) at .DELTA..theta.=0 is
fitted with a 3-Gaussians (lines). The dashed line curve reflects
the peaks associated with a dopant layer identical to those
observed in the static diffraction profile. The resulting
.DELTA.t.sub.w for the prominent Si(400) peak is 2.8.+-.0.4 ns in
agreement with the that obtained from Eq. (3) using experimentally
obtained values of .DELTA..theta..sub.(400)=0.0034.degree.,
.alpha..sub.m=.+-.2.69.degree., and f.sub.m=74.671 kHz.
[0050] In accordance with features of the invention, it is hence
concluded with full confidence that MEMS devices can be
successfully used as an X-ray diffractive optics. This is the first
demonstration of the potential of MEMS diffraction technology in
the X-ray wavelength range to control the pulse train from a
synchrotron radiation source. This opens many new avenues for the
use of MEMS to manipulate and control X-ray radiation. For example,
at any hard X-ray storage-ring or XFEL source 104, the present MEMS
102 can be used to select an X-ray pulse or a stream of pulses from
a pulse-train with a pulse separation of over 2.8 ns. This accounts
for most of the third-generation sources currently operational
worldwide. The X-ray fluence from this optics 102 will be enhanced
from the ultra-small beam dimensions obtainable from the new
generation of storage-ring sources with sub-nm-rad emittance. There
are four control parameters for MEMS operation, namely
.theta..sub.B, .DELTA..theta..sub.(hld), .alpha..sub.m, and
f.sub.m, that add many new capabilities to control the X-ray
energy, pulse selection, and the shape of the pulse. For example,
MEMS optics can be used for time-domain science experiments
requiring a broad range of X-ray energy from about 4 to 50 keV by
choosing appropriate .theta..sub.B. This will commensurately
broaden or narrow the diffractive time-window through the values of
.DELTA..theta..sub.(hld). The values of angular amplitude
.alpha..sub.m can also be varied by orders of magnitude either by
varying the voltage of MEMS excitation pulse or by varying the
ambient pressure in which the device operates. This would allow
selection of X-ray pulses from MHz-GHz sources. Furthermore, MEMS
operation with large values of .alpha..sub.m and f.sub.m will allow
even narrower time windows than reported here, and one can even
reach the ultimate potential to slice 100 ps duration X-ray pulses
by one to two orders of magnitude (similar to laser slicing of
electron bunches) at a storage-ring source, a unique capability for
a broad research community. In summary, the reported performance of
ultrafast MEMS with flexible control over the delivery and the
shape of hard X-ray pulses will herald new opportunities in
time-resolved X-ray studies at any synchrotron radiation
source.
Example Implemented Method
[0051] In accordance with features of the invention, methods
implemented with the MEMS based diffractive optics 102, 200 may be
understood as follows:
[0052] The torsional MEMS device 102, 200 includes a
single-crystal-silicon mass 202 with a smooth surface suspended on
opposite sides by a pair of torsional springs 204, 206. The crystal
202 can be rotated in an oscillatory motion about the torsional
springs 204, 206 by applying an electrical field to the comb-drive
actuators 210. Finite Element Analysis (FEA) was conducted to
determine the modal response of the MEMS device 102, 200. Using
CoventorWare.RTM. simulations show the first harmonic resonance
occurring at 74.6 kHz which was verified from experimental
measurements to be .apprxeq.74.7 kHz. The MEMS device 102, 200 were
fabricated at the commercial foundry MEMSCAP using SOIMUMPS.RTM.
fabrication process with a 25 .mu.m thick device layer. The
measured oscillation amplitude of about .+-.3.degree. required an
application of 70 V.sub.pp.
[0053] The x-ray experiments were performed at Sector 7-ID
beamline, a dedicated beamline for ultrafast x-ray experiments of
the Advanced Photon Source (APS) at Argonne National Laboratory.
The X-ray beam, produced by an undulator source, was
monochromatized by a flat diamond double-crystal monochromator
tuned to photon energy of 8 keV with a bandwidth of
5.times.10.sup.-5. The X-ray beam was not focused and was defined
by a pair of X-Y slits to a size of 100 .mu.m (horizontal).times.6
.mu.m (vertical) before impinging on the MEMS device. The static
rocking curves around the Si(400) Bragg angle was measured by using
a high-resolution diffractometer with a minimum angular step size
of 3.125.degree..times.10.sup.-5. The diffracted photons were
detected by an avalanche photodiode (APD) operated in
photon-counting mode. For dynamic measurement, the transient X-ray
diffraction signal when Bragg condition was met was measured by
another APD but operated in charge-integration mode. The
integration mode is needed because every diffracted X-ray pulse
contained multiple photons. The APD has a fast response with
temporal resolution of approximately 5 ns. The APD signal output
was digitized by a 500-MHz oscilloscope and recorded every 1 ns,
which determines the temporal resolution in determining the delay
time between the MEMS driver pulse and the X-ray pulse diffracted
by the MEMS crystal element. The oscilloscope trace of 1 ms was
measured 20 times to improve the signal-to-noise ratio.
[0054] While the present invention has been described with
reference to the details of the embodiments of the invention shown
in the drawing, these details are not intended to limit the scope
of the invention as claimed in the appended claims.
* * * * *